Find the equation of the circle passing through the points `(1, -1)` and centre at the intersection of the lines `x-y=4 and 2x+3y=-7`

(i) A circle whoe centre is the point of intersection of the line 2x - 3y + 4 - 0 and 3x + 4y - 5 = 0 passes through the origin. Find its equation. (ii) Find the equation of the circle passing through the point (1,-1) and centre at the intersection of the lines (x -y) = 4 and 2x + 3y = -7.

Find the equation of the circle passing through the point (2, 4) and centre at the point of intersection of the lines x-y=4 and 2x+3y=-7 .

Find the equation of the circle passing through the point (2, 4 ) and having its centre at the intersection of the lines x - y = 4 and 2x + 3y + 7 = 0 .

Find the equation of the circle passing through the point (-1,3) and having its centre at the point of intersection of the lines x-2y=4 and 2x+5y+1=0

Find the equation of the line passing through the point (-4,5) and the point of intersection of the lines 4x-3y+7=0 and 2x+3y+5=0 .

Find the equation of the circle passing through the points (0, -1) and (2, 0) and whose centre lies on the line 3x+y=5

Find the equation of the line passing through the point (4,-14,4) and intersecting the line of intersection of the planes : planes :3x+2y-z=5 and x-2y-27=-1 at right angles.

The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x-3y+7=0 and 7x+4y+2=0 is